Modelling of Variable Speed Wind Turbine Connected DFIG:250KW
ANKINEEDU PRASAD PADAMATA1*, DR. GUDAPATI SAMBASIVA RAO2
1Electrical and Electronics Engineering,
Dr. YSR ANU College of Engineering & Technology,
Acharya Nagarjuna University,
Nagarjuna Nagar, Guntur, 522 510, Andhra Pradesh
INDIA
2Department of Electrical & Electronics Engineering,
R.V.R. & J.C. College of Engineering,
Guntur, 522 019, Andhra Pradesh,
INDIA
*Corresponding Author
Abstract: - This manuscript initiates the design and analysis of a doubly-fed-induction-generator (DFIG) linked
to the grid, aiming to assess a wind vitality conversion configuration employing an emulated wind turbine drive
system. The generator's configuration involves integrating the d-q axes reference framework with the stator
flux. Independent management of real, and imaginary power, along with the dc-bus potential at the grid, is
achieved through the field-aligned regulating method. Controlling real, and Quadrature power, as well as DC-
bus potential, is executed using tandem converters at distinct velocities, encompassing sub, syn, and hyper-
synchronous speeds. The effectiveness of these control strategies is validated through the emulation of a
variable-speed wind turbine-connected DFIG, showcasing precise control over DC voltage, reactive power, and
active power.
Key-Words: - Wind turbine; double-fed-induction-generator; DC-bus potential; real and imaginary powers,
tandem converters; Proportional-Integral (PI); Pulse Width Modulation (PWM).
Received: March 19, 2023. Revised: October 12, 2023. Accepted: November 7, 2023. Published: December 31, 2023.
1 Introduction
The growth of any country relies on electric power
generation and consumption, with a focus on
utilizing sustainable energy sources. The transition
to alternative energy sources, is propelled by
anxieties regarding climate disruption, and, the
imperative to decrease Subservience on non-
renewable energy. Wind vitality is gaining
prominence as an especially eco-friendly power
source, given its abundant presence in various
regions and the positive economic outcomes, linked
to substantial vitality production. Consequently, the
reliance on substantial aerogenerators, for energy
production is steadily booming, as emphasized, [1].
The asynchronous generator, with dual feeding, is
notably chosen as the prevailing alternator in wind
turbines, owing to its intrinsic varying speed
features, efficient regulating capabilities, improved
efficiency, and reduced converter requirements for
grid connection. The inherent capability of the
asynchronous generator, with dual feeding resides,
in managing the dynamics, and responsive power
output demands from the load. Although power
dynamics are contingent on wind availability, they
are regulated, even if temporarily, by implementing
instinctive active vitality. This highlights the
significant role of DFIG, as a sustainable power
resource within an integrated framework connected
to the grid. In scenarios wherein minimum of two
viable sources of power to enhance the consignment
of power by regulating the DFIG's dynamics, the
regulation of power is managed to fulfil the grid's
needs. When confronted with an unreliable network
marked by voltage fluctuations, the DFIG can be
operated to generate the required level of imaginary
power for the grid, thereby governing the voltage
profile, as discussed, [2]. The advanced control
capabilities, and the dynamic attributes of dfig’s
based on Variable Speed Constant Frequency
(VSCF) technology, are crucial areas of focus in the
research on wind-energy.
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DOI: 10.37394/232016.2023.18.42
Ankineedu Prasad Padamata,
Dr. Gudapati Sambasiva Rao
E-ISSN: 2224-350X
426
Volume 18, 2023
In a dual-fed configuration, two adjacent
converters fulfil the requirement of providing
energised current to the rotor circuit. Grid-connected
converters (GSC), are linked to the grid, and
function with a three-tier power system or three tier
converters, while sustaining a consistent DC
potential. The stabilized DC voltage serves as the
source of power for the three-tier converter
straightly linked to the rotor circuit, commonly
known as a rotor-side converter (RSC).
The primary role of the GSC, is to elevate a
stable DC potential. However, the GSC also
possesses the capability, to regulate imaginary
power, and offset imaginary power during
unbalanced conditions, [3]. Conversely, the
converter RSC supplies the necessary polarization
current, to that rotor winding, facilitating the
generation of crucial dynamic and imaginary power
capabilities at the stator side.
The production of electric power might undergo,
an increase of 2%–6% when utilizing varying hurtle
wind turbines collated to wind turbines with a
persistent rotational speed, [4]. On the contrary, [5],
there is a potential for increasing power by up to
39%. The German brochure and others, [6], depict
that the power produced with varying hurtle wind
turbines can fluctuate in the range of 3% to
28%distinguished with persistent hurtle wind
turbines, hinging on site conditions, and specific
parameters.. Various studies, including others, [5],
[6], [7], [8], [9], have presented the calculations of
the electric power produced by the dfig. A more
thorough examination of comparing the electrical
circuits in wind turbines is needed. In their research,
[10], investigated power generation across various
methods, including a constant hurtle wind turbine
with an asynchronous generator, a wind turbine with
fully varying hurtle capabilities employing an
inverter-supported asynchronous generator, and a
variable-speed wind turbine utilizing a dfig. The use
of a dual supported asynchronous motor, in
performing as generation mode, enhances the
production of electric power. In the context of a
variable-hurtle system, utilizing a wound rotor
asynchronous motor emanates in a 20% increase in
the power of a dfig, and it experiences a 60%
increase compared to a system with a constant
speed.
It's crucial to emphasize that the investigation
did not consider into account losses associated with
wind distribution, electrical components, and
machinery. Introduced and implemented the double-
supported production strategy for reluctance
machines, inspiring initial attempts to utilize cage
rotor asynchronous motors for similar applications,
[11].
The initial deployment of the dfig was
evaluated, [12]. This implementation utilized a
control technique incorporating a Proportional-
Integral (PI) controller to trigger sinusoidal Pulse
Width Modulation (PWM) with a consistent
switching-frequency. Various researchers have
widely adopted this control scheme. A thorough
exploration of the dfig is suggested, incorporating
the determination of rotor position from voltage and
current parameters, [13].
A notable analysis was conducted with A. The
matrix amalgamation, [14], of the DFIG and its
performance in voltage dip. Additionally,
contribution to the field with additional analysis of
the transient model of DFIG done, [15]. Control
strategy of a dfig, employing hysteresis controllers,
to achieve optimal performance, [16].
The converters RSC, and GSC are analysed
autonomously to investigate the dfig. The RSC can
be executed autonomously, prior to a stable DC-
potential, is supplied from the GSC. A grid-side
controller with the capability to manage the DC
potential amidst irregular source voltage situations
were suggested, [17]. However, this configuration
could not address imaginary power compensation.
The operational point of the GSC can be
established based on the operational point of the
RSC, and operational conditions of the generator.
Introduced analysis sustained by non-linear voltages,
[18], and slip regulators for a dfig tied to the grid.
Explored a straight real, and imaginary power
regulators relying on stator hurtle employing a
hysteresis current controller, [19]. An exemplary
vector governing mechanism to modulate the real,
and quadrature powers generated from a dfig, [20],
was devised. Fundamentally, a controller built upon
a dfig is akin to the traditional AVR/PSS, [21]. This
controller assists in upholding the frequency, and
stoutness of the power system voltage.
The paper outlines a hypothetical
implementation of a supervisory system configured
for a wind generator relying on the dfig. The
supervisory scheme employs field-based control for
monitoring the RSC and utilizes a hysteresis
modulator to regulate the GSC. A crucial and critical
function of the dfig is to sustain the stable
operational state of the DC potential.
The RSC approach facilitates, autonomous
control over both real, and quadrature power in a
dfig through the regulation of rotor-currents. The
effectiveness of these control methods, is closely
tied to the machine electrical attributes, and the
transitions occurring within its reference structure.
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.42
Ankineedu Prasad Padamata,
Dr. Gudapati Sambasiva Rao
E-ISSN: 2224-350X
427
Volume 18, 2023
Nonetheless, the field-oriented control approach,
achieves outstanding control performance,
demonstrating robustness, swift responses in both
transient and steady states, and precision.
DFIG GRID
S2
RSC GSC
Transformer
Fig. 1: Proposed configuration of DFIG system
The GSC propels the passage of power through
the RSC, while offering supplementary quadrature
power. Hysteresis control governs the GSC,
maintaining a consistent DC potential, and ensuring
sinusoidal current along the line. This paper explores
production of power by employing, a dfig, and
analyses the regulating characteristics of its GSC,
and RSC through an active persistent approach. This
study enhances the perception of a dfig associated
wind-turbine application, below various regulating
situations across extensive scale. The configuration
of scheme of envisioned wind-turbine coupled DFIG
system, is depicted in Figure 1.
2 Structure Model
2.1 Windturbine (WT)
A wind-turbine produces electric power, by
capturing and, utilizing the energy from the wind to
drive its coupled asynchronous generator. When the
air currents pass across the blades of the turbine, it
induces lift, and creates a rotational force. These
blades spin the shaft located in the casing, this
rotational force is then, linked to a gearbox. The
gearbox amplifies, the revolving velocity of the
coupled generator, and, subsequently, the generator
utilizes a magnetic field, to transform kinetic form
into electric power.
The power derived from wind is articulated, [22], as:
= 0.5 ρ π (1)
In this context, “ρ” denotes the density of air; "r"
denotes the turbine’ ssword radius; “v” denotes the
wind swiftness, and, “Cp” denotes the coefficient of
power. The coefficient of power is contingent upon
the tip swiftness ratio “λ” and the sword angle “β”.
The tip swiftness proportion is expressed by:
λ=
(2)
Here, 'ω' represents the rotational speed of the
generator.
From the equation (2), the tip swiftness ratio
“λ”, is altered, by regulating the swiftness “ω”,
thereby, controlling the “Cp”, and the induced
output-power, generated by wind turbines. The dfig
is employed in configuring the wind turbines,
enabling the adjustment of velocity to simulate
varying wind velocities.
2.2 Modelling of DFIG
The DFIG is considered akin to the traditional
generator, with a rotor emf. The formulation
provided in [23], defines the expression for the3-ph
DFIG is defined as:
= +
(3)
= +
(4)
= +
(5)
= +
(6)
= (7)
= (8)
= (9)
= (10)
On the other hand, ‘’ represents, the angular
velocity within the coordinated reference
frame., is the slip swiftness, and
‘s’ is the slip,‘’denotes the rotational velocity of
that generator, linked to the kinetic velocity of the
generator through the pair of pole number, as
indicatedwith are
the resistance of stator, resistance of rotor,
inductance of stator, and inductance of rotor
respectively. is the mutual-inductance, and is
the rotational velocity of the rotor. The expressed
formula, the resulting electric torque from the dfig is
expressed as follows.:
=
p( )
=
( )
= -
( ) (11)
Here, 'p' signifies the count of pole pairs.
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.42
Ankineedu Prasad Padamata,
Dr. Gudapati Sambasiva Rao
E-ISSN: 2224-350X
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Volume 18, 2023
The interpretation of the real and responsive
power of the stator as well as rotor for the dfig is
denoted by:
( ) (12)
( ) (13)
( ) (14)
( ) (15)
The power loss linked to the rotor and stator
resistances is not considered in this expression.
3 Control Techniques
The regulating scheme for the dfig, comprises both
grid side, and rotor side controls. The real and
imaginary powers are modulated by RSC, [24], and
the DC link potential regulation as well as imaginary
powers are instilled into the grid and regulated by
GSC.
3.1 Control of Wind Turbine
Now-a-days WECS are much more popular in REs
as they are abundantly available in nature. The
unpredictable characteristics of wind and the varying
hurtle operation in WECS, involves the use of
Variable-Speed Wind Turbines (VSWT) in
conjunction with dfig. The dfig is preferred for its
primacies, like variable speed operation within a
range of approximately± 30% of the nominal-speed,
separation of real and receptive powers, enhanced
energy conversion, and reasonable price. At the
same time, DFIG has a few drawbacks, including the
impact of changes in conditions and sudden changes
in the wind stream. Due to this, the system's
operating point is changed from the most
economical point. Several control topologies are
presented to enhance the performance of DFIG and
VSWT. Traditional controllers like PI (proportional
and integral) are implemented in the major research
studies. Along with the PI controllers, MPPT
techniques are implemented to harness utmost
energy, from the wind. The working of VSWT near
the speed at cut-in is described with the segments,
[25].
Segment 1 (prior to A):
The speed of the wind breeze is below 4 m/s; it
comes under this segment-1, and no power is
extracted. The hurtle of rotor, is customised to the
lowest value of the speed by implementing the
regulator in the angle of the wind turbine blades
below “cut-in speed “at point ‘A’. The operation of
VSWT is considered halt-state and checks for any
rise in wind speed.
Segment-2(A–B):
As the hurtle of wind, crosses the cut-in speed,
mechanical strength emanates with the speed of the
wind breeze, and the VSWT is now interfacing with
the grid. As the wind blows at a lower value of the
speed, the hurtle of the rotor is retained at a reduced
speed. Therefore, the power coefficient ‘Cp’ is
retained at its utmost point. The wind turbine cannot
harvest a viable amount of power from the wind. In
this condition, the tilt in pitch, is generally adjusted
to zero degrees.
Segment-3(B–C):
MPPT functioning of VSWT MPPT can be obtained
when the speed of the rotor is regulated in
accordance with the wind breeze such that optimal
TSR (opt)) is obtained, and the coefficient of power
(Cp)) is achieved to it so maximum value The speed
of the rotor changes, corresponding to the speed of
the wind.
The controller, as depicted in Figure 2, enables
the wind turbine to attain the optimal speed
corresponding to the current wind speed. Various
hurtles of wind breeze, different regulating
techniques, are implemented to obtain the
interrelation between electro-magnetic torque and
the maximal power developed, and the
corresponding optimal rotor speed is obtained.
Segment-4(C–D):
The hurtle of the rotor, approaches a specified
nominal value of hurtle at the point "C" and
maintains the specified value to eliminate huge
instinctive hassle and noise at the VSWT.
Consequently, the TSR is not at its finest value, and
the Cp is less than the value from segment 3 (B-C).
The VSWT sustains, the tilt in pitch, at its optimal
value until the output power (mechanical)
approaches the predefined nominal value.
Fig. 2: Wind speed vs Wind turbine power
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Ankineedu Prasad Padamata,
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Segment-V(D-E)
When the wind speed surpasses 12 meters/sec, the
mechanical output of the Variable-Speed Wind
Turbine is adjusted to a predetermined nominal
value. This is done to mitigate excess current in the
converters (GSC and RSC) and prevent an overload
on the entire drive system. This adjustment is
achieved by controlling the pitch angle.
3.2 Rotor Side Controller
The dfig facilitates power output to both the stator,
and rotor circuits of the machine. Employing such a
machine enables the attainment of an elevated pf
(power factor), even when the speed deviates
slightly above the synchronous speed. Consequently,
these generators can wield without the requirement
for additional bypass-compensating equipment. The
rotor current of the machine, is transformed into the
dq component as follows. The current generates
magnetic lines within the gap, that coincides the
rotational force, to interact with the stator. These
interactions produce constituents of the flux that is
quadrature to the vector. The evolved torque results
from the accumulation of the two vectors, and in this
manner, the current contributes to the evolution of
torque. This current regulates the receptive power
entering the dfig. The precise orientation of the
currents enables the regulation of the active and
receptive power on the stator-side. The pivotal step
involves determining the instantaneous stance of the
rotating magnetic flux, in vector-space to establish
the rotating reference frame. It is established through
Lenz’s law, which posits that the potential in the
stator winding can be obtained from the stator flux
links. Consequently, the stator potential and current
undergo a 3-phase transformation, can be
transformed into the 'αβ' reference frame. The stator
winding flux in the αβ reference- frame is
represented by:
=() (16)
To align the synchronously rotating dq reference
frame with the stator field motion, information about
the rate of change in stator flux can be derived from
the following expression:
() (17)
() = =
;
= (18)
This angle imparts the instantaneous stance of
the revolving magnetic field in the stator. While the
rotor is in motion, and momentarily oriented at a
gradient, the stator magnetic field, with the
mentioned frame fixed to the rotor, is referred to as
the "slip angle". The reference frame is aligned to
establish a simplified mode.
= =; =0 (19)
The torque contingent on the “current” and
its regulation is done by the “voltage ”. The
regulator assesses the “error” beneath the and
and, the reference current and .
This “error” is then subjected to PI regulator to
procure counter balance voltages,and . To
derive the appropriate reference voltage, the
regulator outcome must be balanced with two
decoupling labels.
and as below:
+ σ
σ (20)
+σ
(
(21)
e-j(θs –θr)
P/2
e-j(θs –θr)
PI PI
d/dt d/dt
DFIG IGBT
DC
BUS
PWM
abc
abc
abc
idr_ref
iqr_ref
iabc_s
isαβ
STATOR FLUX
CALCULATION
Ψαβ
θs
ωr
ωs
ωslip
θm
θr
Ψds
ENCODER
irαβ
αβ
αβαβ
αβ
ωslip*
(Lm/Ls* Ψds+σLridr)
ωslipσLridr)
v’dr
v’qr
iabc_r
abc
vabc_s
vsαβ
STATOR ANGLE
CALCULATION
Fig. 3: Structural schema of DFIG-based WECS
In the control mechanism depicted in Figure 3,
the currents in the rotor(, ) constrainedand
governed so that monitoring the corresponding
references, andWith that frame
coordinated with the stator flux, The q(quadrature)-
current governs the true power and the d(direct)-
current governs the receptive power. Therefore, the
q(quadrature)-current is associated to generator
electro mechanical torque, while the d(direct)
current is associated with the voltage profile.
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/ (22)
-2/(3P
) (23)
The PWM regulator functions in the rotor circuit
of the generator, and regulator is executed through
signals of PWM affecting the rotor circuit current,
the stator circuit current, the stator potential, and the
stance of the rotor of dfig, [26].
3.3 Grid-side Controller
The predominant intent of the GSC is to retain a
robust DC link potential, regardless of its amplitude
and the direction of the power flow rotor. To achieve
that, a hysteresis modulator within the reference
framework, oriented with the stator potential
instance, is employed, as illustrated in Figure 2. It
confesses for flexible regulation of the DC potential
and receptive power between the grid, and the
converter.
The power source is restricted by the RSC,
typically generated by employing a Voltage Source
Converter (VSC) tied-up with the grid, specifically
on the stator side of the dfig. A capacitor is
employed to mitigate fluctuations and maintain the
DC potential at a relatively consistent level. A
“PWM” converter is employed to perpetuate the
constant DC link potential. The GSC fulfils the real
power requirements as dictated by the RSC.
Operation with the converter employing reference
flow scheme is facilitated, and consequently,
hysteresis control is adopted. In this control scheme,
the discrepancy between expected and measured
currents is employed to regulate the output potential
of the conventional sine PWM converter, ensuring
the desired power factor, [27]. The architecture of
the GSC is illustrated in Figure 4.
Vdc-ref
GRID
Atan2
(Eβ*/ Eα*)
-90
Eβ*
Eα*
αβ
abc
I
G
B
T
PI
PWM
Hysteresis
Band
dq
abc
Vdc-measured
DC BUS
iabc-g
iabc-g
Fig. 4: Schematic diagram of GSC
The voltages on the grid side in the dq reference
frame are expressed as follows:
= R +L
(24)
= R +L
(25)
Where are the grid emfs in the d-q
frame,,are the GSC emfs in dq frame.,,
are the grid side dq currents, R and L represent the
filter resistance and inductance, respectively, while
'ω' denotes the rotational recurrence. The true, and
receptive powers are stated by:
P =3() (26)
Q=3() (27)
The stance of that grid emf is derived by:
= =
(28)
Here “and are ‘α’ and ‘β’coordinates
in the grid emf, organised by dq emfs making
. Indeed, as the grid emf maintains a steady
amplitude, will also have a steady amplitude.
3.4 Control of DC Link Voltage
The error potential is expressed as:
e = (29)
It’s deviation, is given by:
∆e= (1-) (30)
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or incomplete information in your message. Could
you please provide the specific expression or
information that needs to be modified.
= 3 (30)
The current the DC busin the vector aligned
allusion frame. Therefore, the reference current
is procured from the DC-tied potential blunder ∆e
and its digression are tuned by the gains of PI
controller. To attain a power factor, close to unity at
GSC converter, receptive power value should be
zero, hence 0. Following the dq-to-abc
conversion of the reference current, a hysteresis
regulating scheme can be implemented.
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4 Emulation of VSWT-DFIG
The emulated system comprises a dual excited
asynchronous generator propelled with VSWT. This
generator is accompanied by a back-to-back
connected RSC and a GSC, connected to the grid
through a transformer. The true and receptive power,
extracted with VSWT-DFIG, is controlled with rotor
currents in the RSC. Appropriate electric power
transmission is achieved by governing the DC link
potential, which is further modulated with a GSC.
4.1 Control of Power with,
The wind turbine driven dfig is emulated for (0-7)
sec. Below the synchronous speed, the wind turbine
swiftness is maintained for up to 3 seconds. As
illustrated in Figure 5, the wind turbine operates at
synchronous speed for up to 5 seconds and at hyper-
synchronous speed for up to 7 seconds.
To modulate the powers (true and receptive), the
rotor current components, and are regulated
by tracking the references and
respectively. The reference tracking is
achieved successfully shown in Figure 6.
Inferred from Figure 7 is the regulation of real
and reactive power by adjusting the d-axis current of
the rotor (). The rotor current response under
different speeds is shown in Figure 8.
It is perceived that the true power is modulated
by regulating the (q-quadrature current of rotor)
to track the reference current,the true power
is controlled.
Fig. 5: Rotor Speed characteristics
Similarly, the receptive power is augmented to
maintain power equilibrium with the grid. The
corresponding responses of true power with rotor q-
quadrature current, and receptive power with rotor
d-axis current is depicted in Figure 9 and Figure 10.
Fig. 6: Output of the d-axis rotor current (Idr)
Fig. 7: The output of Rotor q-current (Iqr)
Fig. 8: Rotor current Response (Ir)
Fig. 9: Output of True power with Iqr
Fig. 10: Imaginary power variation with Idr
4.2 Effect of the DC-Link Potential
True power reduces as receptive power increases to
compensate for the total power. Furthermore, a
proportional-integral (PI) controller is employed to
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precisely modulate the DC-link potential, ensuring it
tracks a constant reference as depicted in Figure 9.
To inject true power into the rotor through RSC,
it is essential to retain the DC-link potential as stable
as possible. To track that DC reference potential, a
robust PI regulator is implemented. Regulating the
d-q components of the grid current allows for
attaining a flat voltage profile from the GSC. The
DC link potential profile is depicted in Figure 11.
Fig. 11: Response DC link Voltage
4.3 Impact of Rotor Speed on the Rotor
Currents,
As the wind swiftness is changing continuously, the
variations are emulated by considering different
values of wind speeds. In the wind swiftness range
of 8 m/s to 11 m/s, the rotor speed remains in sub-
synchronous range for 1 to 3 seconds. During wind
swiftness ranging from 11 m/s to 12 m/s, the rotor
speed attaining synchronous speed for a duration of
3 to 5 seconds. In wind speeds ranging from 12 m/s
to 15 m/s, the rotor speed surpasses synchronous
speed, achieving super-synchronous speed for a
duration of 5 to 7 seconds. The rotor speed is tracked
by implementing a robust PI regulator.
Fig. 12: Output of True and Imaginary Powers
Figure 12 shows the true and imaginary power
curves of the DFIG Machine. The d-component
current is robustly controlled and remains unaffected
by variations in rotor swiftness. Only the rotor q-
component current is transformed by the rotor turtle.
The modulated true, and receptive power is achieved
by modulating the rotor “d-q” currents. Hence RSC
is employed to modulate the power with tracking the
rotor, and currents. The true power response is
depicted in Figure 9. The DFIG machine related all
parameters are depicted in Table 1(Appendix).
5 Conclusion
In this paper, control schemes for true, and
imaginary powers are explored in a fluctuating wind
turbine-coupled DFIG. The emulated model covers
sub-synchronous, synchronous, and hyper-
synchronous speeds. The configuration of
tandem(back-to-back) connected RSC and GSC,
direct current control techniques, real and receptive
power modulation, dc link potential regulation with
the help of GSC, and speed control techniques are
implemented and validated at different wind speeds
with simulations.
Further investigation can be enhanced to
implement advanced controllers, providing filters to
reduce harmonic distortion.
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APPENDIX
Table 1. DFIG machine parameters
Power
250KW
Stator Voltage
400V
Stator Current
400V
Rotor Voltage
370A
Poles pair
2
Frequency
50
Rotor speed
1500 rpm
Bus Voltage
600V
Contribution of Individual Authors to the
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Policy)
The authors equally contributed in the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
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WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.42
Ankineedu Prasad Padamata,
Dr. Gudapati Sambasiva Rao
E-ISSN: 2224-350X
435
Volume 18, 2023
